To what email address was his invite sent? Was it your Apple ID/iCloud email or your Gmail?
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bassplayer7Jan 2 '13 at 14:53

To my AppleId email, which is coincedentally also my Gmail
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SamJan 2 '13 at 15:43

Did you add the event to a calendar that is actually synced with Google or maybe (by accident) to a local calendar only?
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MacLemonJan 7 '13 at 22:24

The event got into my Iphone calendar, because I was invited by my squash buddy, so I'm not the 'owner' of the event - which is probably the reason why it doesn't sync, but I want to make sure.
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SamJan 8 '13 at 10:50

If the iPhone calendar syncs to Gmail this event should be synced nonetheless.
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cyphoriousJan 11 '13 at 13:47